SUMP Instruction

SUMP c sigma c1 m1 c2 m2 ...

The linear restraint: c = c1*fv(m1) + c2*fv(m2) + ... is applied to the specified free variables. This enables more than two atoms to be assigned to a particular site, with the sum of site occupation factors restrained to be a constant. It also enables linear relations to be imposed between distances used on DFIX restraints, for example to restrain a group of atoms to be collinear. sigma is the effective standard deviation. By way of example, assume that a special position on a four-fold axis is occupied by a mixture of sodium, calcium, aluminium and potassium cations so that the average charge is +2 and the site is fully occupied. The necessary restraints and constraints could be set up as follows (the program will take care of the special position constraints on the coordinates and Uij of course):

 SUMP 1.0 0.01 1.0 2 1.0 3 1.0 4 1.0 5   ! site fully occupied
 SUMP 2.0 0.01 1.0 2 2.0 3 3.0 4 1.0 5   ! mean charge = +2
 EXYZ Na1 Ca1 Al1 K1             ! common x, y and z coordinates
 EADP Na1 Ca1 Al1 K1             ! common U or Uij
 FVAR ... 0.20 0.30 0.35 0.15    ! starting values for free variables 2..5
 ...
 Na1 ... ... ... ... 20.25 ...   ! 0.25 * fv(2)  [the 0.25 is required for
 Ca1 ... ... ... ... 30.25 ...   ! 0.25 * fv(3)  a special position on a
 Al1 ... ... ... ... 40.25 ...   ! 0.25 * fv(4)  four-fold axis, i.e. site
 K1  ... ... ... ... 50.25 ...   ! 0.25 * fv(5)  symmetry 4]

Similar SUMP restraints may be used when elements are distributed over several sites in minerals so that the elemental composition corresponds (within suitable standard deviations) to an experimental chemical analysis.